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介质垂向非均匀性和内在各向异性都会导致反射时距曲线偏离双曲形状。基于传统双曲时差方程的时间域成像方法不能准确归位远偏移距或大入射角地震波能量。将已有非双曲时差方程总结归纳为级数展开逼近、时移双曲近似、反椭圆近似和正交多项式逼近4类,面向Kirchhoff叠前时间偏移推导了级数展开四阶逼近、时移双曲近似和反椭圆近似的双平方根时差方程。数值试验结果表明,反椭圆近似在垂向变化横向各向同性(VTI)介质中有很高的精度,它在各向异性介质时间域成像方面有大的应用潜力。
Both vertical and internal anisotropy of the medium cause the curve to deviate from the hyperbolic shape when reflected. The time-domain imaging method based on the traditional hyperbolic hertransduction equation can not accurately locate the far-offset or large-angle seismic energy. Based on Kirchhoff prestack time migration, the fourth-order approximation of series expansion was deduced when the existing non-hyperbolic time difference equations were summarized as series expansion approximation, time-dependent hyperbolic approximation, inverse elliptical approximation and orthogonal polynomial approximation Double Square Roots Time Difference Equation of Moving Hyperbolic Approximation and Anti - elliptic Approximation. Numerical experiments show that the inverse elliptic approximation has a high accuracy in vertical-variation transversely isotropic (VTI) media and has great potential for imaging in the time-domain of anisotropic media.